Lines.cs

using System.Windows;

// Base class for lines
abstract class LineBase
{
	// First and second point of the line
	public readonly Point p0, p2;

	public override string ToString()
	{
		return $"{{ {p0} }} -> {{ {p2} }}";
	}

	protected LineBase( Point a, Point b )
	{
		if( !( a - b ).LengthSquared.isNormal() )
			throw new ArgumentException( "The points are too close, they don't define a line." );
		p0 = a;
		p2 = b;
	}

	// Test if the parameter is inside the line.
	protected abstract bool isInside( double param );

	// Intersection algorithm goes here
	public bool intersects( LineBase that, out double paramThis, out double paramThat ) { ... }

	// Returns p0 * ( 1.0 - param ) + p2 * param
	public Point at( double param ) { ... }
}

class Line : LineBase
{
	public Line( Point a, Point b ) : base( a, b ) { }

	protected override bool isInside( double param )
	{
		// Lines are infinite in both directions
		return true;
	}
}

class Ray : LineBase
{
	public Ray( Point a, Point b ) : base( a, b ) { }

	protected override bool isInside( double param )
	{
		// Rays are infinite in one direction
		return param >= -0.0;
	}
}

class Segment : LineBase
{
	public Segment( Point a, Point b ) : base( a, b ) { }

	protected override bool isInside( double param )
	{
		// Segments are limited on both ends.
		return param >= -0.0 && param <= 1.0;
	}
}

static class LinesExt
{
	public static double? intersectionParam( this LineBase i, LineBase that )
	{
		bool res = i.intersects( that, out double m0, out double m2 );
		if( !res )
			return null;
		return m0;
	}

	public static Point? intersectionPoint( this LineBase i, LineBase that )
	{
		bool res = i.intersects( that, out double m0, out double m2 );
		if( !res )
			return null;
		return i.at( m0 );
	}

	public static bool intersects( this LineBase i, LineBase that )
	{
		return i.intersects( that, out double m0, out double m2 );
	}
}